Symplectomorphisms mirror to birational transformations of the projective plane

Abstract: We construct a non-finite type four-dimensional Weinstein domain $M_{univ}$ and describe a HMS correspondence between distinguished birational transformations of the projective plane preserving a standard holomorphic volume form and symplectomorphisms of $M_{univ}$. The space $M_{univ}$ is universal in the sense that it contains every Liouville manifold mirror to a log Calabi-Yau surface as a Weinstein subdomain; after restricting to these subdomains, we recover a mirror correspondence between the automorphism group of any open log Calabi-Yau surface and the symplectomorphism group of its mirror. This is joint work with Ailsa Keating.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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